Method and system for determining a boundary surface network

ABSTRACT

A method is disclosed for determining a boundary surface network of the tubular object. In an embodiment, a representation of the tubular object is initially provided on the basis of image data and local dimension information is provided for points of the representation. A subdivided division structure presentation of the tubular object with division cells is then created, which based on the local dimension information, including a different spatial extent. Finally a boundary surface network is derived on the basis of the division structure presentation. Also described are a boundary surface network determination system and a division structure determination system for performing such a method.

PRIORITY STATEMENT

The present application hereby claims priority under 35 U.S.C. §119 toGerman patent application number DE 10 2012 203 117.0 filed Feb. 29,2012, the entire contents of which are hereby incorporated herein byreference.

FIELD

At least one embodiment of the The present invention generally relatesto a method for determining a boundary surface network of a tubularobject, a separation structure determination system for determining aseparation structure for a tubular object and a boundary surface networkdetermination system for determining a boundary surface network of atubular object.

BACKGROUND

The pictorial presentation of surfaces of a tubular object with acomplicated shape, such as the bronchial system, a vascular system orother hollow organs, forms the basis for a plurality of analyses,especially in the clinical field. Numerous problems can be detected forexample with the aid of a fly-through of the hollow organ, thesimulation of the course of a fluid or the more detailedthree-dimensional presentation of critical areas, so that a furtherprocedure can be defined especially in relation to the medicaltreatment. This requires that the most complete information possibleabout the topological structure of the tubular object is available. Suchinformation about the topological structure can be obtained for examplewith the aid of imaging methods, such as computed tomography or magneticresonance tomography for example. Without further processing the imagesand presentations thus obtained are only suitable to a limited extent ornot suitable at all for the analyses. The multidimensional descriptionof the surface of the hollow organ with the aid of a boundary surfacenetwork presentation or surface network modeling, abbreviated hereafterto “boundary surface network”, delivers the desired geometricalinformation and for the above analyses should also reproduce details ofthe surface to a sufficient extent.

Methods are known for calculating a boundary surface network of a holloworgan in precise detail, which describe the surface with the aid ofnumerically complicated and computing-intensive interpolations. Thecalculated boundary surface networks are generally characterized by anoutstanding level of accurate detail. Because the enormous computingeffort involved however, these presentations cannot be calculated withina short time or instantaneously, so that real-time manipulations, forexample for “what if” analyses, in order to simulate the insertion of astent into a blood vessel for example, only enter into consideration toa limited extent on the basis of these methods for calculating aboundary surface network.

The necessary speed in the determining of the boundary surface networkcan be achieved by simplifying the numerical effort with the aid of amodel of the surface that is as simple as possible. By contrast with“model-free” interpolation computation methods which are based on theanalysis of point clouds, such models approximate the hollow organ ofwhich an image is to be produced with the aid of a set of simplegeometrical shapes such as cylinders or spheres for example. Thisapproximation however only rarely delivers a boundary surface network ofthe hollow organ which reproduces critical details, especially in thearea of branching points, approximately correctly. As a result of thisan exact dimensioning of geometrical changes of the vascular system isunsuitable for diagnosis and treatment planning of a pathology.

For simulation of a course of the fluid it is for example necessary forthe entire geometry and especially branches of the hollow organ to bereproduced as identically as possible to their natural state, and aboveand beyond this the boundary surface network calculated shouldfrequently be “watertight”, i.e. it may not feature any openings whichare not present in reality.

Results of the model-based determination of a boundary surface networkonly rarely meet these requirements however, since especially theadaptation of the simple geometrical basic form is complicated when thesize conditions of part structures of the hollow organ vary greatly andwhen branches occur. Undesired artifacts in the boundary surface networkdetermined occur at branches as a result of simple geometrical basicmodel elements such as spheres or the like frequently used for modelingprojecting into each other and structures which are not present inreality are modeled in the interior of the boundary surface networkdetermined. These boundary surface networks are for example only usableto a restricted extent for the said “fly-through” applications.

SUMMARY

At least one embodiment of the invention provides an option for rapiddetermination of a boundary surface network of a tubular object, whereindetails of the surface structure can be reproduced as precisely aspossible and the generation of undesired structures inside the boundarysurface network is preferably entirely avoided.

A method is disclosed for determining a boundary surface network of atubular object, a separation structure determination system is disclosedfor determining a separation structure for determining a boundarysurface network of a tubular object and a boundary surface networkdetermination system is disclosed for determining a boundary surfacenetwork of the tubular object.

Inventively a method of at least one embodiment, including thefollowing, is proposed for determining a boundary surface network of atubular object:

An initial step comprises the provision of a representation of thetubular object based on image data, in such cases the tubular object canespecially have a number of branches. Preferably, as mentioned at theoutset, this involves a hollow organ, especially a bronchial system orvascular system. The image data of the object can for example have beendetermined by a computed tomogram of a magnetic resonance tomograph,i.e. ultimately the data involves measurement data of these tomographysystems or measurement data reconstructed therefrom. Preferably the datainvolves three-dimensional image data or a set of two-dimensional slicedata which cover a three-dimensional volume. A representation of thetubular object is to be understood as a dataset which in some wayreproduces the geometrical structure of the object, if necessary evenonly at specific selected positions or in sections. An example of thisis the center line representation explained further on in this document.Basically the representation can however also involve the measured,unmodified or edited (for example filtered) image data itself.

A further step of at least one embodiment of the inventive methodcomprises the provision of local dimension information for points of therepresentation. This local dimension information can be provided forexample on the basis of the image data or on the basis of therepresentation itself. In particular it is also possible for points ofthe representation to be assigned a number of items of local dimensioninformation. Furthermore it is also conceivable for the local dimensioninformation to be a direct part of the representation. The localdimension information can for example involve a diameter or a radius ata specific point (i.e. local location) of the hollow organ. Thecorresponding point of the hollow organ is then assigned to a specificpoint or object of the representation.

A subsequent step comprises the creation of a divided separationstructure representation of the tubular object with division cells whichhave different spatial extents based on the local dimension information.The division structure representation can especially be divided uphierarchically, i.e. for example inherently dependent, and is especiallypreferably generated recursively. The division structure comprises adivision into division cells, which do not intersect and wherein thecombination of the division cells represents the entire space of thetubular object to be mapped. In the recursive embodiment of the divisionstructure representation this applies in particular to division cellswhich have each been determined in a last step of the recursive method.

The space of the tubular object to be mapped corresponds to an originalspace which is defined in a “global coordinate system”. This globalcoordinate system is defined in relation to a measurement space of thetomography system underlying the image generation, especiallyindependently of the position of the tubular object in the measurementspace of the tomography system. This means that the origin of the globalcoordinate system is for example the center of the measurement space anda first coordinate axis runs in the direction of the longitudinal axisthrough the measurement space, while the other two coordinate axes areorthogonal to this first axis and orthogonal to one another. To simplifyfurther calculations, this is preferably an orthonormal right-handedsystem.

In a further step of at least one embodiment of the inventive method theboundary surface network is ultimately derived on the basis of thisdivision structure representation.

With the aid of at least one embodiment of the invention it is nowpossible for the first time, independently of a fixed division structuresize, to define a locally dependent size of the division cells, which inthe final analysis determines the accuracy of the detail reproduction ofthe boundary surface network. In at least one embodiment of the method,the dimensions of the division cells correspond to a local sampling ratefor sampling the surface of the hollow organ which, if the structure ofthe hollow organ requires this locally, is increased or reducedrespectively.

On the one hand it is ensured in this way that at least one embodimentof the method is not too computing-intensive, so that a rapidcalculation of the boundary surface network is possible. On the otherhand it can be reliably prevented in this way that artifacts arisethrough differences in size of local structures, which for example leadto the said problems in the branching area. Thus it is especiallyeffective to use at least one embodiment of the inventive methodessentially as a model-based method, as will be described in greaterdetail below.

In accordance with at least one embodiment of the invention a divisionstructure determination system for determining a division structurerepresentation of a tubular object is also proposed. This has an inputinterface which is embodied to provide a representation of the tubularobject. A further input interface or an input interface identical tothis input interface of the division structure determination system isembodied for providing local dimension information for points of therepresentation. The system further comprises a division structuredetermination unit which is embodied to create a divided divisionstructure representation of the tubular object with division cells. Thedifferent division cells can in this case, as previously mentioned, havedifferent spatial extents, based on the local dimension information.

In addition a boundary surface network determination system fordetermining a boundary surface network of the tubular object is proposedin accordance with at least one embodiment of the invention. This systemcomprises the previously described inventive division structuredetermination system and in addition to this a network determinationunit which is embodied for deriving the boundary surface network of thetubular object based on the division structure representation.

Significant parts of the division structure determination system and/orof the boundary surface network determination system can preferably berealized in the form of software on a suitable programmable processorunit, for example a diagnosis station, with the appropriate storageoptions. This relates in particular to the division structuredetermination unit and the network determination unit. The inputinterfaces, which can also be embodied as a single common interface, canfor example involve interfaces for selection and transfer of data from adata memory disposed within the division structure determination systemand/or the boundary surface network determination system or connectedtherewith via a network—if necessary also using a user interface.Furthermore the systems can each have output interfaces in order totransfer the data created to other units for further processing,presentation, storage etc. A largely software-based realization,especially of the division structure determination unit and of theboundary surface network determination unit, has the advantage thatimage data processing units or the like already used previously can beupgraded in a simple manner by a software update, in order to work inthe inventive manner.

In this regard, at least one embodiment of the invention is directed toa computer program product which for example is stored in atransportable memory and/or is provided for transmission via a networkand so is able to be loaded directly into one or more memories of thedivision structure determination system. The computer program productcomprises program code sections to execute all steps of at least oneembodiment of the method for determining a division structurerepresentation and/or for determining a boundary surface network of thetubular object in accordance with at least one embodiment of theinvention when the program is executed in the division structuredetermination system.

Further especially advantageous embodiments and developments of theinvention emerge from the dependent claims as well as from thesubsequent description, wherein the independent claims of one claimcategory can also be embodied similarly to the dependent claims ofanother claim category.

As already noted at the outset, model-based methods for determining aboundary surface network offer a particular speed advantage. In adevelopment of at least one embodiment of the invention one or morelocal segment objects are therefore adapted to the representation, inorder to achieve a largely model-based description of the surface of thehollow organ. Preferably the topological structure of the segmentobjects is selected from a group of basic bodies (or model basic bodiesrespectively).

These basic bodies will also be referred to below as (graphical)primitives or groups of primitives. They can for example include asphere, a truncated cone, a semicircle or similar or in the simplestcase only consist of a simple geometrical body. What the primitives havein common is that their surface shape can be described mathematically ina simple manner and thus a possibility for rapidly calculating points ofthe surface of the hollow organ is achieved. A mathematicallysimple-to-calculate surface shape is produced for example if a finitenumber of computing steps suffices for exact description of the surfaceand for example a closed function can be specified to describe thesurface.

As will especially be explained below, at least one embodiment of theinvention also provides opportunities for adapting different segmentobjects to one another. This means the primitives selected foradaptation can have a different topological structure from one another.For example a truncated cone can be selected in combination with asemicircle for adaptation to the representation.

As well is the advantage of rapid determination of the surfacestructure, the segment object division also offers the possibility ofimproving the division structure representation. For example with theaid of the segment objects the local dimension information required inaccordance with the invention can be derived or obtained, which then forexample corresponds to a minimum radius of the segment object. With atruncated cone this could for example be the radius of the coveringsurface, with a sphere it could be the radius of this sphere.

The local dimension information can in its turn directly represent acriterion for deriving the locally differing extent of the divisioncells or on the basis of the local dimension information thus formed, acriterion for locally differing extent of the division cells can beformed, which ultimately determines the quality of the adaptation of thedivision cells to the surface form of the tubular object.

A development of at least one embodiment of the inventive divisionstructure determination system or of the boundary surface networkdetermination system accordingly further comprises a segment objectdetermination unit which is embodied to adapt one or more segmentobjects to the representation.

As mentioned, at least one embodiment of the invention is based on theidea of adapting the spatial extent of a division cell to localdimension information about the tubular object. Preferably a spatialextent of a division cell can be determined at a location, especially ofthe origin space so that the division cell would be able to be fittedcompletely, i.e. in its entirety, into a local reference object, i.e. asphere, an ellipse or the like, for example.

The local reference object, which is preferably not calculated forboundary network determination can be defined in such cases based on thelocal dimension information, especially so that the reference object inits turn is able to be fitted into the tubular object or also into thelocal segment object at the relevant location.

In other words the reference object describes a locally-relevantreference range of the local dimension information provided, i.e. thereference object makes possible a simple check as to whether the size ofthe division cell is defined so that bounding edges of the division cellcan have an intersection point with the surface section of the holloworgan. This means in particular that the method for determining thespatial extent of the division cells is such that the given conditionsfor possible adaptation of a reference object are fulfilled. In order tocarry out the said checking it can be sufficient to determine a fewreference variables of the reference object and compare them with thedimensions of the division cell. In the case of a spherically-shapedreference object, its radius can for example be compared as acharacteristic variable with the dimensions of the division cell.

As an alternative a combination of one or more characteristic variablesof the reference object can be included for the comparison.

In an example embodiment, the representation comprises a center linerepresentation of the tubular object having a number of center pointsdisposed on a center line spaced apart from one another. Preferably forcenter points of the center line representation a contour of the tubularobject in a surface perpendicular to the center line is also specifiedas part of the center line representation. This can involve anapproximated contour, for example in the form of a circle, or anellipse, but also a free-form contour. Thus, at each center point, localdimension information is also given with the center pointrepresentation. The local dimension information can for examplecorrespond to a radius of the tubular object in the area of the centerpoint which is predetermined by the contour. With an irregular contourfor example the largest or smallest “radius” (or radial distance fromthe center point to the contour) could be used as local dimensioninformation. The center line representation reflects the topology andlocal dimensions of the tubular object in an advantageous manner, sothat a representation is available which can be presented and processedwith little computing effort. A representation in the form of a centerline representation thus preferably forms the basis for further stepsfor determining a boundary surface network.

Then for example one or more segment objects in each case could bedisposed between two center points arranged on the center linerespectively or adapted to the center line presentation. The segmentobjects can for example likewise be selected on the basis of the localdimension information or make different local dimension informationavailable. As will also become clear, the determination of the divisionstructure representation is ultimately undertaken on the basis of thecenter line and especially on the basis of the segment object. Thesegment objects or their topological structure are preferably selectedfrom the graphic primitives described above.

Especially preferably the division structure representation comprises anoctree, and the division cell is formed by a cuboid spatial area. Thiscuboid can especially involve a cube. The division into thecuboid-shaped division cells offers the advantage that a seamless,non-overlapping division of a Euclidian space is produced.

In accordance with a development of at least one embodiment of theinvention a bounding box, which can be n-dimensional, is determined foreach segment object, i.e. can be embodied especially also merely as arectangle. The bounding box contains a respective segment objectpreferably exclusively the assigned segment object, i.e. the boundingbox is preferably selected just large enough for the segment object tofit into it.

This bounding box is used especially to predetermine an (n-dimensional)spatial area, in which the surface of the segment object is calculated.The calculation can be performed especially so that, for each point ofthe bounding box, it can be specified where the surface of the segmentobject is located in relation to this point. The restriction of thespace in which the segment object is determined provides the opportunityof improving the speed of the creation of the boundary surface network.In this way in particular, regions not needed for calculation of thesurface of the tubular object can be excluded, and it is clear thatpoints that do not lie in a bounding box lie at so great a distance fromthe surface of the tubular object that they can remain unconsidered inthe presentation of the boundary surface network. Because of the simplegeometrical form of the bounding box this can be established quickly.

In a development of at least one embodiment of the invention, to createthe division structure presentation, starting from a start divisioncell, a preferably hierarchically-divided subdivision of the startdivision cell is undertaken step-by-step from or into preferablyhierarchically-dependent division cells.

This subdivision of a division cell is performed until such time as anabort criterion is fulfilled by the division cell, which is based on thedimension information. In such cases different abort criteria can betaken into consideration cumulatively or alternately.

With a first abort criterion a division cell is no longer divided up ordivided when the division cell exhibits no coverage with a segmentobject and/or a bounding box.

With a second abort criterion a division cell is no longer furtherdivided when a local division limit value is reached or undershot by thedivision cell.

With the aid of these abort strategies it is thus possible to excludefrom a further subdivision spatial areas which are free from surfaceelements of the tubular object, and furthermore a local adaptation tothe shape of the tubular object, especially its curve radii, by thelocal division threshold value.

Especially preferably the local division threshold value is based on thelocal dimension information and can accordingly be selected to bedifferent in each case for a number of division cells.

Preferably the local division threshold value can be selected from thelocal dimension information.

As an alternative or in addition it is conceivable for the localdivision threshold value to be determined from a combination with thelocal dimension information, i.e. for the local dimension information tobe a parameter in the determination of the local division thresholdvalue. Furthermore it is likewise conceivable, as an alternative or inaddition, for the local division threshold value to be an extreme valueof the local dimension information or to be based on an extreme value ofthe local dimension information.

If the division cell for example exhibits a coverage with a bounding boxwhich surrounds a truncated cone spherical segment object, the localdivision threshold value can be defined by the minimum of the radii ofthe two end surfaces, i.e. the radius of the coverage surface, or thisradius is used for determining the local division threshold value. It isthus insured that a further subdivision of the division cells occursuntil such time as the boundary surface of the division cell has anintersection point with the surface of the smallest locally presenttubular object.

A variable division of the space can thus be achieved, which suppressesan unnecessary division of division cells in the division structurepresentation. Thus in its turn a boundary surface network can becalculated more quickly.

Based on the idea that the local division threshold value defines aspatial sampling interval which specifies a spatial distance in whichthe surface of the tubular object is sampled, depending on thecomplexity of the tubular object, it can be advantageous to scale thissampling interval. The local division threshold value based on thedimension information for each division cell determined independently ineach case can be defined for this purpose by a combination with ascaling factor defined jointly for a number of division cells.

For example with the aid of the common scaling factor the smallestachievable size of a division cell can be defined so that it alwaysundershoots the local dimension information, so that closer sampling ofthe surface of the tubular object is achieved, without local differencesin the dimensions of the division cells being lost in the process, i.e.the locally relevant density of the sampling of the surface of thetubular object is scaled at the same time. A scaling factor determinedin this manner thus allows any given sampling accuracy. Furthermore ascaling factor thus determined guarantees the detection of all branchesof the tubular object. This means, the topological structure of thetubular object is reproduced entirely correctly in each case.

In the same way it is however also possible that the smallest achievablesize of the division cell always undershoots the local dimensioninformation, so that a degree of compromise betweentopologically-correct imaging of the boundary surface and speed isachieved. If however the local threshold value for the division cellsize is adhered to, the creation of the boundary surface network istopologically reliable in any event, i.e. all vessels are represented.In order to ensure that two vessels are not presented as one if thedistance between them lies below the sampling accuracy, in addition tothe smallest vessel dimension information, distance information can alsobe included as a local dimension information. Thus vessels which lieclose to each other will also be visualized as separate structures.

In particular the combination of the scaling factor with the localdivision threshold value can involve a multiplication of the localdivision threshold value by the scaling factor.

As already mentioned at the start, model-based methods for determining aboundary surface network are frequently prone to artifacts in the regionof branches. An especially preferred option for ameliorating theseartifacts is the description of segment objects, i.e. simple primitives,with the aid of a signed distance function. This is preferablydetermined within the bounding box. Each segment object is thereforeassigned a separate signed distance function. The signed distancefunction in this case specifies for each interrogation point, i.e. apoint in the local space which preferably lies within the bounding box,the distance from the surface of the assigned segment object.

Thus in addition to model-based reproduction of the surface of thetubular object, an implicit description of the surface of the tubularobject is also provided. On this basis segment objects adjoining eachother can be combined into a common surface description. As will becomeclear later, this especially offers the option of describing a number ofsegment objects touching one another so that the outer surface of thecombination volume of the segment objects, i.e. of the model of thetubular object, can always be determined.

The signed local distance function can preferably also be included tocreate the division structure presentation and/or to adapt the localdivision threshold value. Above and beyond this or in addition thesigned local distance function can likewise be used for creating theboundary surface network, especially based on the division structurepresentation.

In order to always describe an outer surface of a number of segmentobjects adjoining each other, especially preferably on the basis of anumber of signed local distance functions, a global signed distancefunction can be determined. In this function the function values of theglobal signed distance function at a specific interrogation pointrepresent an extreme value of the signed local distance function valueswhich are included for forming the global signed distance function atthis interrogation point. The following considerations are to be takeninto account here:

The global signed distance function should provide information aboutwhich points are disposed outside a segment object, which points are onthe surface of a segment object and which points within a segmentobject. As well as the described distance information the topology canthus be determined with this method in a simple manner with the aid ofthe global signed distance function.

The extreme value can therefore be formed for example from the minimumof the function values of a number of local signed distance functions.This is especially sensible when points outside a segment object aredescribed by a positive distance value from the surface of the segmentobject and points within the segment object are described by a negativevalue of the signed local distance function.

The minimum thus determined, i.e. the extreme value, thus also providesthe information as to whether an interrogation point lies within avolume which is described by the combination of the segment objects, oron the surface of the combination volume region or outside the volume ofthe combination of the segment objects. In particular all points areidentified which are disposed within the combination volume. In thismanner it is possible to emulate the surface of the tubular object withthe aid of a number of different segment objects, wherein the surface ofthe combination volume of a number of segment objects lying furthestoutwards is always taken into consideration for determining the boundarysurface network.

The artifacts mentioned at the start within the created boundary surfacenetwork can be very effectively avoided in this way.

In a development of at least one embodiment of the invention the globalsigned distance function can be determined to take account of aplurality of bounding boxes. This means that the global signed distancefunction is merely determined in the combination of the bounding boxeswhich are assigned to the respective segment objects. The global signeddistance function is thus then based for example on the local distancefunctions in these bounding boxes, so that rapid calculation of theglobal signed distance function is also made possible.

The distance values from the surface of the segment object or of thetubular object determined with the aid of the local and/or the globalsigned distance function can be included for determining the localdivision threshold value. The local division threshold value preferablydetermined on the basis of at least one signed local distance functionand especially preferably on the basis of the global signed distancefunction can be determined in a development by a function value of thesigned local distance function and/or of the signed distance functionbeing defined in a center of the division cell involved. This divisioncell center can for example be defined by the intersection point of thesurface normals which are each placed in the center of the surfaces, theboundary surfaces of the division cell, or as the center of gravity ofthe corners of the division cell.

For example the global distance function in the center of a cubic octreecell can be evaluated in this way and compared with the size of thecubic octree cell. The comparison with the dimensions of the octree cellmakes it possible to establish in a simple manner whether the closestsurface of the tubular object is located within the octree cell or not.This comparison can thus represent a third abort criterion for thesubdivision of the octree cells, since a further division can then beconsidered when the closest surface of the tubular object lies withinthe Octree cell.

In an example modification of at least one embodiment of the invention atriangle surface network based on the determined division structurepresentation is created or determined as the boundary surface network.The division structure presentation reproduces the size or determines a“maximum meshing width” of the boundary surface network, in order to mapall locally relevant structures. With the aid of a global signeddistance function assigned to the respective division cell a triangularsurface network can then be derived in a simple manner. A methodconsidered for this purpose is for example the so-called “marchingcubes” method, in which it is determined at corner points of thedivision cell in each case, based on the global signed distancefunction, whether this corner point is located within, outside or on asurface of the tubular object.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be explained below once more in greater detail withreference to the enclosed figures based on example embodiments. In thesefigures the same components are provided with identical referencecharacters in the different figures, in which:

FIG. 1 shows a very simplified flow diagram for an example embodiment ofthe inventive method for determining a boundary surface network,

FIG. 2 shows example embodiments the geometrical primitives for use asgraphic primitives,

FIG. 3 shows an example embodiment of the adaptation of geometricalprimitives to a center line presentation,

FIG. 4 shows an example embodiment for the definition of a bounding box,

FIG. 5 shows a diagram of different possible intermediate steps for anexample embodiment of a derivation of a division structure presentation,

FIG. 6 shows a more detailed diagram of a step from FIG. 5,

FIG. 7 shows an example embodiment for the adaptation of a referenceobject to a division cell,

FIG. 8 shows an example embodiment for the definition of a global signeddistance function,

FIG. 9 shows an example embodiment for the definition of an abortcriterion for division of a division cell,

FIG. 10 shows an example embodiment for determining a mesh of a boundarysurface network based on a global indicator function within theframework of a “marching cubes” method,

FIG. 11 shows an example embodiment for a center line presentation withan ordered row of contours for a section of a bronchial tree and twocontours highlighted therein,

FIG. 12 shows a detailed view of a section of the center linepresentation from FIG. 11 with the two highlighted contours,

FIG. 13 shows an example embodiment for the transformation of twocontours not crossing one another from an origin space into a unityspace,

FIG. 14 shows an example embodiment the definition of a global indicatorfunction,

FIG. 15 shows an example embodiment for a center line presentation withan ordered row of contours for a section of a bronchial tree as depictedin FIG. 11, but with two contours crossing one another highlightedtherein,

FIG. 16 shows a detailed view of a section of the center linepresentation from FIG. 15 with the two highlighted contours,

FIG. 17 shows a further example embodiment for the transformation ofcontours into a unity space as depicted in FIG. 13, but with the twocontours crossing one another,

FIG. 18 shows a presentation of a possible boundary surface network fora section of a vascular tree, and

FIG. 19 shows an example embodiment for a boundary surface networkdetermination system.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

The present invention will be further described in detail in conjunctionwith the accompanying drawings and embodiments. It should be understoodthat the particular embodiments described herein are only used toillustrate the present invention but not to limit the present invention.

Accordingly, while example embodiments of the invention are capable ofvarious modifications and alternative forms, embodiments thereof areshown by way of example in the drawings and will herein be described indetail. It should be understood, however, that there is no intent tolimit example embodiments of the present invention to the particularforms disclosed. On the contrary, example embodiments are to cover allmodifications, equivalents, and alternatives falling within the scope ofthe invention. Like numbers refer to like elements throughout thedescription of the figures.

Specific structural and functional details disclosed herein are merelyrepresentative for purposes of describing example embodiments of thepresent invention. This invention may, however, be embodied in manyalternate forms and should not be construed as limited to only theembodiments set forth herein.

It will be understood that, although the terms first, second, etc. maybe used herein to describe various elements, these elements should notbe limited by these terms. These terms are only used to distinguish oneelement from another. For example, a first element could be termed asecond element, and, similarly, a second element could be termed a firstelement, without departing from the scope of example embodiments of thepresent invention. As used herein, the term “and/or,” includes any andall combinations of one or more of the associated listed items.

It will be understood that when an element is referred to as being“connected,” or “coupled,” to another element, it can be directlyconnected or coupled to the other element or intervening elements may bepresent. In contrast, when an element is referred to as being “directlyconnected,” or “directly coupled,” to another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between,” versus “directly between,” “adjacent,” versus“directly adjacent,” etc.).

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of exampleembodiments of the invention. As used herein, the singular forms “a,”“an,” and “the,” are intended to include the plural forms as well,unless the context clearly indicates otherwise. As used herein, theterms “and/or” and “at least one of” include any and all combinations ofone or more of the associated listed items. It will be furtherunderstood that the terms “comprises,” “comprising,” “includes,” and/or“including,” when used herein, specify the presence of stated features,integers, steps, operations, elements, and/or components, but do notpreclude the presence or addition of one or more other features,integers, steps, operations, elements, components, and/or groupsthereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Unless otherwise defined, all terms (including technical and scientificterms) used herein have the same meaning as commonly understood by oneof ordinary skill in the art to which example embodiments belong. Itwill be further understood that terms, e.g., those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art andwill not be interpreted in an idealized or overly formal sense unlessexpressly so defined herein.

Spatially relative terms, such as “beneath”, “below”, “lower”, “above”,“upper”, and the like, may be used herein for ease of description todescribe one element or feature's relationship to another element(s) orfeature(s) as illustrated in the figures. It will be understood that thespatially relative terms are intended to encompass differentorientations of the device in use or operation in addition to theorientation depicted in the figures. For example, if the device in thefigures is turned over, elements described as “below” or “beneath” otherelements or features would then be oriented “above” the other elementsor features. Thus, term such as “below” can encompass both anorientation of above and below. The device may be otherwise oriented(rotated 90 degrees or at other orientations) and the spatially relativedescriptors used herein are interpreted accordingly.

Although the terms first, second, etc. may be used herein to describevarious elements, components, regions, layers and/or sections, it shouldbe understood that these elements, components, regions, layers and/orsections should not be limited by these terms. These terms are used onlyto distinguish one element, component, region, layer, or section fromanother region, layer, or section. Thus, a first element, component,region, layer, or section discussed below could be termed a secondelement, component, region, layer, or section without departing from theteachings of the present invention.

FIG. 1 shows a very simplified flow diagram for an example embodiment ofan inventive method for determining a boundary surface network of thetubular object.

In an initial step I of the method first of all a representation 10 ofthe tubular object is made available. For this purpose image data BD isanalyzed, which has for example been measured with a computed tomographysystem or created with a magnetic resonance tomography system. Typicallythis image data BD features two-dimensional slices through the tubularobject. The combination of a number of these two-dimensional slices inthis case allows deductions to be made about the three-dimensional shapeof the tubular object. The original image data can principally be usedas the representation 10 of the tubular object. Since however thevolumes of image data are very large, a representation 10 of the tubularobject is mostly created from said data in the form of a center linepresentation. Based on the image data BD in such cases a center line isplaced in each tube section of the tubular object, and at regular butalso at irregular intervals center points are disposed on the centerline.

FIG. 11 shows a schematic of a section of a center line presentation ofa bronchial tree as an example. In this case each of the center pointsis assigned a contour C1, C2 in a plane perpendicular to the centerlines at the location of the center point (the contours C1, C2 are onlyshown enlarged here to mark them out from the contours at the othercenter points), which represents the dimensions of the tubular object inthis plane. This can involve simplified geometrical contours C1, C2approximated to the real contour of the tubular object at the respectivecenter point, such as circles or ellipses, or as in FIG. 11, can involvefree-form contours C1, C2, as will be explained later. I.e. through thecenter line presentation an ordered series of contours C1, C2 at the rowof center points will be made available here.

Through the contour C1, C2 the center point is also assigned localdimension information 15 in each case, which for example describes thedistance to the closest surface of the tubular object, i.e. the shortestdistance to the surface or, with a circular contour C1, C2, simply theradius. A center point can also be assigned a number of items of localdimension information 15, so that each center point can be associatedwith one or more contours of the tubular object. Center points to whicha number of contours C1, C2 are assigned, can for example be present inthe area of branches of the tubular object.

Different methods for creation of center line presentations based onimage data are known to the person skilled in the art. One method isexplained for example in the German patent application DE 10 2009 006414 B3, the entire contents of which are hereby incorporated herein byreference.

In a subsequent step II a segment object 20 is then fitted betweencenter points on this center line following immediately after oneanother. The segment objects 20 can for example involve geometricallysimple-to-describe primitives (known as graphical primitives), forexample a cylinder, a sphere 21, a cone, a truncated cone 22 or also asemicircle 23, some of which are shown in FIG. 2.

Especially conducive to a rapid calculation of the boundary surfacenetwork of the tubular object in this case is that an equation for sucha simple segment object can be specified in a closed form or as set ofeasily-definable boundary surfaces, which make it possible to calculatethe distance of an interrogation point from the surface of the segmentobject. In FIG. 11 this is highlighted on the basis of the markedcontours C1, C2, which are approximated here by a truncated-cone-typesegment object 20.

As will be explained again later, an embodiment of the invention alsomakes it possible to transfer this concept to any given free-formcontours. This means that segment objects 20, which are fitted betweenthe center points, can also be based within the framework of theinvention on so-called free-form contours.

In this case the fitting of a segment object between center points canalso be realized by transformation functions TPS1, TPS2 being determinedfor the contours C1, C2, so that these can be transformed from theorigin space (shown in FIG. 11) into a unity space. Based on thetransformed contours C1, C2 a unity space segment object 20E can thus becreated in the unity space so that in turn the aforementionedrequirement of a simple calculation of the surface shape is sufficient.In this case each unity space segment object 20E, which corresponds to aset of consecutive contours (in FIGS. 13 and 17 for example twoconsecutive contours C1, C2 in each case) is assigned a transformationfunction TPS1 or TPS2. The contours C1, C2 belonging to a unity spacesegment object 20E, are transformed in this case with the sametransformation function TPS1 or TPS2 into the unity space. In the unityspace an equation in closed form or a set of simple-to-define boundarysurfaces can thus be specified with the aid of which the distance of aninterrogation point in the unity space from a surface of the unity spacesegment object 20E can be calculated.

In a subsequent step III of the example embodiment of the inventiondescribed in FIG. 1 based on the segment object 20, 21, 22, 23 (or basedon the unity space segment object 20E in conjunction with thetransformation function TPS1, TPS2) a hierarchically-divided divisionstructure presentation 100 of the tubular object will be created.

In the preferred embodiments shown here the division structurepresentation 100 involves an octree 100 with cubic division cells 200.However the invention is not restricted to such embodiments.

Other division structure presentations 100 are likewise conceivable.Thus for example a quadtree or a combination of quadtrees would also beconsidered. The form of the division cells 200 can likewise deviate.Thus for example a pentagonal basic surface can be provided for thedivision cells.

The octree 100 forms a complete presentation of the origin space, i.e.in the example embodiment, especially of a space, which is described inso-called global coordinates. These global coordinates represent acoordinate system independent of the object observed and will usually bedefined in relation to the measurement space of the imaging system used,i.e. the origin of the global coordinate system lies for example in thecenter of the imaging system and the coordinate axes can be correlatedwith the characteristic device axes.

In addition it is likewise conceivable that the origin space refers to acoordinate system, which is assigned to the image data BD, wherein theorigin coordinates of the origin space for example lie in one of thecorners of an image.

FIG. 5, explained later, shows an example for the creation of an octree100.

The cubic division cells 200 of the octree 100 have a different spatialextent in this case. This different extent is determined in the exampleembodiment, based on the local dimension information 15, as will bedescribed later in greater detail.

In particular in this example embodiment a local signed distancefunction is determined for each of the segment objects 20 or the unityspace segment object 20E. This local signed distance function LFdescribes in each case the distance for an interrogation point from asurface of the segment object or to the surface of the unity spacesegment object 20E.

In a further step IV, based on the octree and—at least indirectly—on thebasis of the local signed distance function LF, the boundary surfacenetwork 1000 of the tubular object is derived from the object. Such aboundary surface network 1000 is for example shown in FIG. 18 for asection of a vascular tree.

As will be described in more detail later, intersection points of anumber of segment objects 20 are approximated with the aid of a globalsigned distance function GF or a global indicator function GIF. Theglobal indicator function GIF or the global signed distance function GFis based in this case respectively on the local signed distance functionfor the determined segment objects, independently of whether this wasdetermined in global coordinates or in a unity space.

FIG. 3 shows an example embodiment of a representation 10 of a verysimple tubular object O in detail. The representation 10 is in this casea center line representation 10. For a topological reproduction of thetubular object O in this example embodiment, on account of a branch of anumber of center lines separated from one another are used, especially afirst center line M1 and a further center line M2. As an alternative thebranch could however also be represented by center lines coinciding, sothat practically a single branching center line, similar to a treestructure, represents the tubular object O.

The center lines M1, M2 shown each extend in a straight line in sectionsbetween center points 111, 112, . . . 117 disposed at irregularintervals on the respective center lines M1, M2, wherein each of thecenter points 111, . . . , 117, as described above, is assigned at leastone item of local dimension information and/or contour C1, C2, C3, C4.The local dimension information at the same time specifies the radialextent of a number of segment objects 20, which are each fitted betweentwo consecutively-disposed central points 111, . . . , 117 on one of thecenter lines M1, M2. These segment objects 20 reproduce in modelingterms sections of the surface shape of the tubular object O. A modelingdescription especially has the advantage that the complexity of thedescription of the surfaces of the tubular object can be restricted, sothat a rapid calculation of the boundary surface network is possiblewith it.

The calculation is especially optimized by the segment object 20, asdescribed in conjunction with FIG. 2, being selected from a group ofgraphical primitives. In FIG. 3 for advantageous approximation andmodel-type description of the surface shape of the tubular object O, anumber of segment objects 20 topologically different from one anotherare fitted between two center points 111, 112, 113, 114, 116, 117following one another on the center line representation 10.

Assigned to a first center point 111 disposed on the center line M1 hereis a first radius r1 as local dimension information 15. The first radiusr1 is specified in this case by the center line presentation. In thesame way however it is also conceivable for the dimension information 15to be taken directly from the image data BD on which the center linepresentation 10 is based. This first radius r1 here defines a contour C1of the basic surface of a first truncated cone 22 assigned to the firstcenter point 111. This contour C1 lies in a plane which is perpendicularon the center line section to a neighboring further center point 112.The outer surface or assigned length of the truncated cone is specifiedby the distance between the first center point 111 and the furthercenter point 112. An item of local dimension information 15 assigned tothis center point 112, which comprises a second radius r2, defines theradial extent of the covering surface of the truncated cone 22 in thiscase. At the same time this dimension information determines a secondcontour C2 assigned to the further center point 112, which is assignedto the covering surface. The center line presentation makes availablecenter lines M1, M2 with an ordered series of contours C1, C2 at theircenter points 111, 112, 113, 114 as well as dimension informationassigned to these lines.

A segment 23′ of a hemisphere adjoins the cover surface of the saidtruncated cone 22 with a half diameter which likewise corresponds to thesecond radius r2. This hemisphere segment 23′ closes a gap which wouldotherwise remain for a further truncated cone disposed after thehemisphere segment 23′. This subsequent truncated cone 22 is disposedbetween the further center point 112 and a subsequent center point 113of the center line M1 as follows. The second and third radii r2, r3assigned to these center points 112, 113 as well as the distance betweencenter points 112, 113 specify base surface, outer surface and coversurface of the subsequent truncated cone 22 in the manner described inrelation to the first truncated cone 22. In addition the furthercontours C3 and C4 are defined by the basic and cover surfaces of thistruncated cone.

As the example embodiment of FIG. 3 shows, with the aid of twotopologically-different segment objects 20, such as truncated cone 22and hemisphere segment 23′, the number of segment objects necessary formodeling the tubular object O with a prespecified accuracy of theimaging of the surface shape is drastically reduced, so that in turn thecalculation speed of the boundary surface network can be optimized.

A further center line M2 starts In the area of the branch of the objectO in the vicinity of the main center line M1, so that the center point115, which forms the start point of the further center line M2, lieswithin the first truncated cone 22 adapted to the first center line M1.The branching, further center line M2 thus touches or intersects asegment object 20 assigned to the first center line M1. The furthercenter lines M2 have local dimension information 15 assigned in asimilar manner in their turn to each of their center points 115, 116,117, especially radii, so that based on the center line M2 and thedimension information 15, the surface of the tubular object O isapproximated in its turn by truncated cones 22 and semicircle segments23′.

As can further be seen from FIG. 3, the surface of the tubular object O,especially in the area of the intersection, cannot be modeled in asimple manner by the unification of the surface of the segment objects20. For example a truncated cone assigned to the second center line M2would project into a number of segment objects 20 of the first centerline M1.

To avoid this and yet still obtain or even strengthen the advantage ofrapid calculation of a model-type description of the surface, thesegment objects 20 determined on the basis of the local dimensioninformation 15 are used within the framework of embodiments of theinvention for creating an octree.

The octree, as already explained above represents a recursively created,hierarchical image of the origin space PS to which the representation 10of the tubular object O is related.

In the creation of an octree the origin space in which the observedobject O is located is divided up recursively into division cells, i.e.bounding boxes or bounding cubes so that their unification reflects theentire observed origin space. As previously mentioned, in this case therecursive division can be undertaken on the basis of the segment objects20 adapted to the center line presentation 10 and thus especially on thebasis of the local dimension information 15. The cubic bounding boxesdetermined then have in accordance with the invention a differentspatial extent depending on the local dimension information 15. Thelocal dimension information 15 can in addition to its assignment tosegment objects in this case however be used in numerous manners todefine the spatial extent of the bounding boxes.

Here especially each segment object 20 can be assigned a bounding box30, which completely encloses the respective segment object 20. It isespecially advantageous for the bounding box to enclose the respectivesegment object 20 spatially as tightly as possible, as is shown by wayof example in FIG. 4 for a compound segment object 20*with a truncatedcone 22 and with two hemispheres connected to it. The bounding box 30corresponds to the minimum box which can enclose the segment object 20*.The truncated cone 22 in this case—as previously described in accordancewith FIG. 3—based on the first radius r1 and the second radius r2 andbased on the center line M1 with the center points 111, 112 adapted tothe center line presentation 10. The spatial dimensions of the boundingbox 30 described and upper limit of the extension of the segment object20*, so that the dimensions of the bounding box 30 can be included todefine the spatial extent of the division boxes—as described below

Further information which can be advantageous for defining the spatialextent of the division boxes is the local signed distance function LFalready mentioned in conjunction with FIG. 1. This then its turn isdefined within the spatial area of the bounding box 30 for a segmentobject 20 written into said box and describes the distance of a giveninterrogation point in the bounding box 30 from a closest surface of therespective segment object in relation to the interrogation point. Asindicated in FIG. 4, in the example embodiment the local signed distancefunction LF is defined so that, for interrogation points which lieoutside the volume of the segment object 20*, it delivers positivedistance values while interrogation points which lie within the volumeof the segment object 20*, are assigned negative distance values.Accordingly interrogation points which lie on the surface of thetruncated cone 22 have a function value of zero of the local signeddistance function LF. Thus the local signed distance function LF, aswell is a monotonously progressing distance function via the sign of theresulting function value for an interrogation point, also providesrelative position information of this interrogation point in relation tothe surface of the segment object 20* and thus also in relation to thelocation of the interrogation point in relation to the surface of thetubular object. For time-optimized calculation of the local signeddistance function no function value is assigned to interrogation pointswhich lie outside the bounding box 30 of the segment object 20*, sincethese points are irrelevant in the further method for deriving theboundary surface network of the tubular object.

Because of the advantageous “simple” geometric surface form of thesegment objects 20, which—as already mentioned—can be described with theaid of a closed function of a set of simple-to-define boundary surfaces,it is likewise possible to define the local signed distance function LFon the basis of the closed function or the set of simple boundarysurfaces. The preferred analytical calculation of the local signeddistance function LF thus only occupies little time so that anespecially fast determination of the boundary surface network ispossible.

The local signed distance function LF is thus based, as described, onthe respective segment object 20*, i.e. especially on the localdimension information 15 assigned to the segment objects or segmentobject 20*. The local signed distance function LF contributes, as willbe explained in greater detail later, to defining the expansion of theoctree cells, so that this expansion ultimately in its turn is based onthe local dimension information. In addition, in accordance with theexample embodiment described, further criteria for defining the extentof the bounding boxes 200 can be included in order to achieve adetermination which is as exact as possible and yet still rapid of theboundary surface network. In particular taking account of the localsigned distance function in the definition of the spatial extent of thedivision cells 200 of an octree will be shown by way of a concreteexample below. FIG. 5 shows for this purpose a division of the originspace PS into division cells 200, initially based on the dimensions ofthe respective bounding box 30 of the segment objects adapted to thecenter line presentation.

A start division cell 200S, which comprises the complete origin space PSwhich contains the tubular object O to be modeled, is divided uprecursively into a number of division boxes 200, which are shown herefor reasons of clarity only in a two-dimensional view. Also shown in theorigin space PS in accordance with the center line presentation of thetubular object O are bounding boxes 30 defined as described previously,which each form a minimal box-shaped envelope of segment objects, whichmodel the tubular object O in the origin space PS.

In a first division step T1 the start division cell 200S is firstdivided up into eight division boxes 200 with the same dimensions, inorder to obtain the “octree representation” 100 of the origin space PS.In the view depicted in FIG. 5 and the four of the division boxes 200can be seen, which will also be referred to for the octree hereafterwith “octree cells”. One of the octree cells 200 this case is free frombounding boxes 30 and does not thus contain any spatial area of thetubular object O, i.e. is “object-free”, while the further octree cells200 are “object-containing”.

In a subsequent, second division step TII all object-containing octreecells 200 which are covered by a bounding box 30 are in their turn eachdivided up into octree cells 200 with identical dimensions. Theobject-free octree cell 200 on the other hand is not divided up anyfurther, so that an end measurement of this octree cell is reached.Division boxes, which have reached their end measurement in thehierarchically divided division structure presentation 100 will bereferred to below as “leaves”, correspondingly for the octree 100 as“octree leaves” 201.

In the example embodiment shown in FIG. 5 the described procedure isrecursively repeated in two further division steps TIII, TIV. During therecursive repetition, based on the criterium of the coverage of octreecells 200 with bounding boxes 30, further spatial areas are determinedthat are object-free and thus in their turn form octree leaves 201.

In order to achieve the best possible approximation to the topology andthe dimensions of the tubular object O, the division of the octree 100is however also undertaken on the basis of further criteria, whichdefine the size of the octree leaves 201. In particular for thispurpose, based on the local dimension information 15, a local divisionthreshold value Rth is determined, which defines the spatial extent ofthe octree leaves 201.

As already explained for example in conjunction with FIG. 4, eachsegment object 20 is assigned at least one item of local dimensioninformation 15, which can be formed for example for truncated cones 22from the first radius r1 and/or the second radius r2. So that thesegment object 20 locally reaches at least the dimensions of the smallerof the two radii r1 or r2, the local division threshold value Rth isadvantageously defined by the smaller of the two radii r1, r2 and thuscorresponds in this case to an extreme value, the minimum of the localdimension information 15.

This is for example additionally illustrated in FIG. 6 for a number ofbounding boxes 30 with assigned (not shown for the purposes of clarity)segment objects. A number of minima min1, min2, . . . , min4, i.e.extreme values of the local dimension information 15 assigned tobounding boxes, are compared for this purpose. As can be seen in FIG. 6,one of the octree cells 200 has a coverage with a bounding box 30, towhich a first minimum min1 is assigned. The same division cell 200likewise additionally has a coverage with a bounding box 30 which asecond minimum min4 of the local dimension information is assigned(which is marked for the sake of clarity some distance away from theoctree cell 200 concerned, but correctly for the bounding box 30concerned). The first dimension min1 is smaller in this case and thesecond dimension min4. This octree cell 200 is now subdividedrecursively into a number of smaller octree cells 200 with identicaldimensions until such time as a local division threshold value Rth,based on the minimum of the two minima min1, min4, is undershot. Thelocal division threshold value Rth, can thus likewise be defined basedon an extreme value of the number of local items of dimensioninformation in 15 of a number of segment objects 20 and/or of a numberof bounding boxes 30. In this case only bounding boxes 30 or segmentobjects 20 are taken into consideration which have coverage with theoctree cell 200. The local division threshold value Rth is determined onthe basis of all locally-relevant segment objects 20. The correspondingminimum is thus what is referred to as a “locally-relevant minimum” or a“locally-relevant extreme value”. The local division threshold value Rthis accordingly an estimation of the locally-relevant smaller structureof the tubular object O in the area of the respective division cell 200.

A development of an embodiment of the invention based on this idea isillustrated with the aid of FIG. 7. The local division threshold valueRth should preferably in this case reach at most the dimension of thelocally-relevant smaller structure of the tubular object, and theestimation of the local division cell threshold value Rth should be so“conservative”, i.e. careful or minimal, that a segment object definedbased on a local dimension information only partly covers the divisioncell 200 if necessary, i.e. the octree cell 200 should be smaller thanthe segment object. This is especially advantageous since, as will bedescribed below, based on the coverage information of the division cellswith segment objects or bounding boxes, the boundary surface network canbe determined especially quickly.

In order to guarantee this conservative estimation, the local divisionthreshold value Rth can be defined so that a smallest division cell 200created therewith would be able to be fitted at a location (i.e. anoctree leaf) completely into a local reference object RO lying at thislocation. The local reference object RO preferably for its part involvesan object of which the surface or shape is described by a closedfunction or a set of easily-definable boundary surfaces, i.e. is easy todescribe. In the example embodiment with cubic octree cells 200 thereference object RO involves a sphere. Depending on the basic shape ofthe division cell 200 however, other reference objects RO can also beselected as an alternative. For example when the division cell 200 is inthe shape of a cube, rotation ellipsoids, cylinders or the like can besensible in order to deliver an estimation that can be determinedrapidly as to whether the dimensions of the division cell 200 aresmaller than those of an overlapping segment object.

The spherical reference object RO is defined on the basis of the localdimension information or the locally-relevant minimum minr so that it isable to be fitted into the tubular object O or the local segment object20 in the area of the division cell 200. The sphere thus correspondshere to a largest object that would be able to be fitted into thesegment object 20 or the tubular object in the area of the division cell200, and thus defines an upper threshold for the local divisionthreshold value Rth. An upper threshold for the local division thresholdvalue Rth can in this example embodiment accordingly be estimated asfollows.

$R_{th} < {\min_{r}{\cdot \frac{\sqrt{3}}{2}}}$

In this case it is to be stressed at this point that thelocally-relevant minimum minr merely involves an example for an item oflocal dimension information 15. The upper threshold value can also bedefined for other segment objects by other local dimension informationwith the aid of the described calculation.

In the example embodiment, for all object-containing octree cells 200, afurther subdivision is undertaken recursively until the length of theside of the octree cells 200 in each case achieves or undershoots thelocal division threshold value Rth thus defined. In this way it isguaranteed that the dimensions of the octree leaves 201 are always lessthan the dimensions of locally-relevant structures of the tubular objectO. This definition of the local division threshold values Rth thereforealso guarantees that each segment object, at least at one point,intersects with the boundary surface of an octree leaf 201. This means,as will become clear subsequently, that for each segment object 20 atleast one representation is created in the boundary surface network1000. The definition of the dimensions of the octree leaves 201 in thisway can thus be referred to as “topologically reliable”.

Starting from this topologically reliable definition of the localdivision threshold value Rth, the representation of the boundary surfacenetwork can be improved even further. If for example segment objects aremore closely spaced than the local division threshold value Rth, it isnot guaranteed that actually separated segment objects will not stillcoalesce with each other in the creation of the boundary surfacenetwork.

In order to improve this situation, the local division threshold valueRth, which is determined as previously described on the basis of thelocal dimension information, can be defined with the aid of a commonscaling factor. The scaling factor will be referred to below as the“quality factor” or abbreviated to QF and scales all local divisionthreshold values Rth of the octree by a common factor so that the localdivision threshold value Rth is thus jointly scaled as shown below buthowever will be individually defined for each octree cell 201:

$R_{th} < {\frac{1}{QF} \cdot {\min_{r}{\cdot \frac{\sqrt{3}}{2}}}}$

The quality factor is freely selectable as a quality parameter.

For values QF<1 the topologically reliable creation of the octree willno longer be achieved. If this is not necessary however a further speedadvantage in the calculation of the boundary surface network can beachieved therewith.

For values QF<=1 a further reduction of the local division cellthreshold value Rth for all octree leaves by a common factor isundertaken so that, although somewhat more time is necessary forcalculation with these values, the quality of the detail presentationcan be further improved.

The definition of the octree, especially with a quality factor QF>=1, aswell as a topologically reliable presentation, also has the advantagethat the relevant spatial area for presenting the boundary surfacenetwork is significantly restricted. This restriction can also occurwithout the previously described local signed distance function LF oranother implicit description of the surface of the tubular objectalready having to have been evaluated.

If the number of segment objects have an intersection area with a commonoctree leaf, this could lead to a large number of superfluous divisionsof the octree into octree cells which lie completely within a volumeenclosed by the tubular object. In order to avoid this, a furtherimprovement with a criterion for defining the dimensions of the octreeleaves can be achieved, which ensures that the octree leaves always haveat least one overlapping area with the surface of the tubular object.

As already indicated, a criterion for defining the local divisionthreshold value Rth can also be provided by the local signed distancefunction LF. In order to take account of intersections of segmentobjects in the local division threshold value Rth, a global signeddistance function GF can thus be defined by the local signed distancefunctions, especially with a number of overlapping segment objects,which is preferably defined within the determined minimum bounding boxof the overlapping segment objects as described previously.

A determination of the global signed distance function is shown ingreater detail with the aid of FIG. 8.

In the example embodiment a number of segment objects formed from spheresegments 23′ and truncated cones 22 once again overlap and map a sectionof a tubular object. Each of the segment objects, the truncated cones 22and the sphere segments 23′, is in this case assigned a local signeddistance function LF in an assigned bounding box 30, whichsimultaneously delivers via the sign of its function value relativeposition information as to whether an interrogation point is locatedwithin or outside the segment objects concerned. Interrogation pointswhich deliver a negative function value of the local signed distancefunction LF, lie within the segment object, interrogation points towhich a positive function value is assigned lie outside the segmentobjects and interrogation points with function values of zero lie on thesurface of the respective segment object.

A global signed distance function GF which, for each interrogation pointof a division cell, is formed by the minimum value of the local signeddistance function LF of the segment objects overlapping with thisdivision cell, likewise correctly reproduces this location information.All points which lie within the unification volume of the segmentobjects are described with a negative function value of the globalsigned function GF, all points which lie outside the unification volumeof the segment objects are described with a positive function value ofthe global signed function GF, and all points which lie on the surfaceof the unification volume of the overlapping segment objects 20 areassigned a function value of the global signed distance function GF ofzero. The global signed distance function GF, as well as giving thedistance of an interrogation point from the surface of the unificationvolume thus also reproduces relative location information with regard tothe unification volume of a number of segment objects with thereproduction of the relative location information this thus also fulfilsthe function of what is referred to as a global indicator function GIFfor the unification volume of the overlapping segment objects. At thesame time the surface of the unification volume of the segment objectscan be defined exactly.

It should be noted at this point that the global signed distancefunction GF thus defined does not undertake any interpolation over thesurface of a number of segment objects. With the aid of the globalsigned distance function GF it is therefore also possible to describesharp edges of segment objects or of the surface of the unificationvolume of the number of segment objects.

It should also be pointed out that the local signed distance function LFcan also be defined so that interrogation points which lie outside asegment object can be reproduced with negative function values andinterrogation points which lie within the segment object with positivefunction values. In this case, unlike in the example embodiment shown,the global signed distance function GF for an interrogation point wouldhave to be formed from the maximum of the function values of the localsigned distance functions for the respective interrogation point.

FIG. 9 illustrates the use of the global signed distance function GF orof the global indicator function GIF for defining the dimensions of adivision cell.

At each of the corner points of the division cell 200 the global signeddistance function GF or an item of relative location information isevaluated with the aid of the global indicator function GIF. Ifdifferent leading signs are present at the corner points, it is uniquelyclear that the delimitation of the division cell intersects with thesurface of the tubular object or the unification volume of a number ofsegment objects. For as long as this condition is fulfilled a furthersubdivision of the division sells 200 can thus take place, until finallythe edge length of the division cells 200 reaches the local divisionthreshold value Rth. If for this octree cell 200 with an edge lengthwhich corresponds to the local division threshold value Rth, there arestill different leading signs at the corner points, an octree cell 200is defined which intersects the surface of the tubular object and doesnot have to be further divided, i.e. represents an octree leaf. With theaid of the local signed function it can thus be established that arecursive division also continues to make sense and does so for at leastuntil such time as the local division threshold value Rth is reached.

As an alternative to this procedure, the global signed distance functionGF or an item of relative location information can also only beevaluated with the aid of the global indicator function when thedimensions of the octree cell 200 have reached or undershot the localdivision threshold value Rth.

A difference in the sign of the global signed distance function GF orthe global indicator function GIF for one of the corner points fromother corner points of the octree cell with both procedures basicallyrepresents a unique criterion that this octree cell contributes to thedescription of the surface of the tubular object and accordingly must betaken into account in the creation of the boundary surface network.

The case depicted in FIG. 9 shows however that in the reverse case, if(as shown here) there is no change of leading sign, it cannot be clearlyexcluded that the surface of the tubular object does not run through thedivision cell. FIG. 9 shows a concrete example of a case in which therehas already been a division of the octree cell up to the divisionthreshold value Rth, i.e. no further subdivision would now take place inwere this to be the only checked abort criterion. Even if there were tobe an additional check for the division being aborted that all cornerpoints of the division cells have the same leading sign for the globalindicator function GIF, a surface of the object only projecting on oneside into the division cell would not be taken into consideration in thecreation of the boundary surface network.

Therefore in the example embodiment, as a further improvement fordetermining whether a further division of the octree cell 200 up to thelocal division threshold value Rth is sensible, the global signeddistance function GF for an interrogation point in the center Z of thedivision cell 200 assigned to the division cell 200 is determined inaddition.

The center Z of the division cell 200 is defined in this case by thecommon intersection point of the central perpendiculars of the boundarysurfaces of the division cell 200. The center Z corresponds in this caseto a geometrical center point of the division cell 200. This definitionof the center Z can be undertaken not only as here for octree cells 200,but also for other topologies of division cells 200 in a similar manner.

Based on the function value of the global signed distance function GFfor the central interrogation point in center Z, a comparison is madebetween the distance of the central interrogation point Z from thesurface of the tubular object and the dimensions of the division cell200. If the distance of the interrogation points is below one of thedimensions of the size criterion assigned to the division cell 200concerned, it is highly certain that it has an overlapping area with thesurface of the tubular object. In this case a further division of thedivision cell 200 is undertaken. In a variant of the method the furtherdivision is therefore only aborted if the testing of this criterion alsoreveals that the surface does not project into the current octree cell.

The edge length of the cubic division cells amounts in the case shown toprecisely Rth. The size criterion that is used for this comparison isgiven for the cubic division cells of the example embodiment by thevalue

${\frac{\sqrt{3}}{2} \cdot R_{th}},$Wherein, if the checking is undertaken before the local divisionthreshold value is reached, instead of Rth, the edge length of thedivision cell at the time of the checking can be used in the sizecriterion. A further division is undertaken in this case if the functionvalue of the global signed distance function GF, for an interrogationpoint in the center Z of the division cell, undershoots this sizecriterion, i.e.

${{GF}(Z)} < {\frac{\sqrt{3}}{2} \cdot R_{th}}$

In the example embodiment shown the size criterion is thus defined asthe (greatest) distance from the central interrogation point to one ofthe corner points of the division cell and here corresponds to half ofthe space diagonal of the cubic octree cell 200.

It is thus possible, with the aid of the method described, to create alocally-adaptive division cell structure, whereby the dimensions or thesize of the division cells are defined as locally different, based ineach case on a number of criteria. In particular a division structure iscreated based on local dimension information, which ensures that eachoctree leaf, having dimensions based on a predetermined local divisionthreshold value Rth, has at least one intersection point with thesurface of the tubular segment object. In addition, with the aid of theglobal indicator function GIF or the global signed distance function GF,an option is provided for exact calculation of the surface of thetubular object for each of the division cells 200.

FIG. 10 shows the calculation of a section of the boundary surfacenetwork 1000 based on a division cell 200 of the division structurerepresentation. With the aid of the global indicator function GIF or theglobal signed distance function GF, for the octree vertices, i.e. thecorners of the octree cell 200, a distance or at least a leading sign isdetermined as to whether the octree vertex involved is located inside oroutside or on the surface of the tubular object. Then, based on thisinformation, the known “marching cubes” method can be applied todescribe surface sections of the tubular object as the network and toderive a boundary surface network. With the aid of triangles, which arefitted into the division cell 200 in each case, the surface of thetubular object is emulated in the spatial area assigned to therespective division cell 200.

In the example shown in FIG. 10 the global signed distance function GFhas a negative function value at one of the right-hand upper corners ofthe octree cell. It is thus clear for this corner point that it lieswithin the tubular object.

At the further corners of the octree cell the function value of theglobal signed function GF is positive in each case. These corner pointsthus lie outside the tubular object. Based on this information, atriangular surface is fitted into the octree cell 200, which accordinglytakes account of the relative location information, formed by therespective leading sign of the global signed distance function GF. Sincethe size of the octree cell 200 is already very well adapted in relationto the locally-relevant dimensions of the tubular object an outstandingrepresentation of the tubular segment object is already achieved by thetriangle network produced.

In accordance with the method of the previously described exampleembodiments for creating a boundary surface network 1000, the segmentobjects 20 are each selected from a group of primitives in order to makea mathematical description of the surface of the segment object possiblein a simple manner.

However, as already briefly mentioned, this concept can also betransferred in a preferred variant of the method to complicated-shapedsections of the tubular object, which are more advantageously describedby planar non-self-intersecting freeform contours.

FIG. 11 shows a section from a center line presentation 10 of an aorticarch and branching arteries. As stated, this center line presentation 10comprises in the origin space PS (in the global coordinator system) anordered series of contours C1, C2 on the center points disposed on acenter line through the respective branch of the arteriovascular system.Each of the contours C1, C2 is linked here with one or more items oflocal dimension information. In a section marked by dashed lines, twofree-form contours C1, C2 are highlighted for example, which inaccordance with the previously described method, could each beapproximated by a truncated cone-type segment object 20.

In FIG. 12 this marked section is shown enlarged, so that these contoursC1, C2 are shown in greater detail. It can be seen here that theapproximation to the surface shape of the arterial blood vessel tree bya truncated cone-shaped segment object 20 only succeeds locallyrelatively roughly for the series of contours C1, C2 shown.

FIG. 13 shows an improved option for simple creation of a boundarysurface network, for example with the method described above, even ifthe surface of the bronchial tree is described by complex free-formcontours C1, C2.

For the contours C1, C2 a transformation function TPS1 from the originspace PS in the global coordinates system into a unity space US isdetermined, wherein the transformation function TPS1 transforms thecontours C1, C2 in each case into a plane E1, E2 in the unity space US.

The transformation function TPS1 in this case respectively forms theconsecutive contours C1, C2 defined in the origin space PS in the unityspace to contours with a circular bounding edge K1, K2 lying in therespective plane E1, E2.

Furthermore the bounding edges K1, K2 here define an essentiallycylindrical or oblique cylinder-shaped unity space segment object 20E,since the corresponding planes E1 and E2 are disposed essentially inparallel to one another in the unity space. I.e. the delimitation edgesK1, K2 do not have any common point in the example embodiment shown inFIG. 13.

Distance calculations for the unity space segment object 20E forinterrogation points of the unity space are therefore possible in asimple manner, since the signed distance function of the unity spacesegment object 20E is able to be defined on the basis of the closedfunction or the set of simple boundary surfaces. The advantages alreadydescribed in relation to the use of primitives relating to thedefinition of a local signed distance function can thus be transferredto the unity space segment objects 20E. The mathematically complicatedinterpolation of the surface of free-form contours for calculating asegment object which would otherwise be needed in the origin space PS inthe previously described method for creating a boundary surface networkis thus avoided in the unity space without any significant disadvantagesarising here.

In this case use is made of the fact that in accordance with thepreviously described method for determining a boundary surface network,a relative location information for an interrogation point of the globalcoordinate system (i.e. information as to whether the point lies inside,outside or on the surface of the object) can suffice to derive adivision structure presentation and to determine a boundary surfacenetwork of the tubular object.

In the example embodiment the transformation functions TPS1, TPS2 arebased on what is referred to as a thin plate spline transformation.These types of transformations are known in principle to the personskilled in the art. A description can be found for example in IEEETransactions On Pattern Analysis and Machine Intelligence, Vol. 11, No.6, June 1989: “Principal Warps: Thin-Plate Splines and the Decompositionof Deformations”, the entire contents of which are hereby incorporatedherein by reference. These transformations from the origin space PS intothe unity space US, although they do not contain distance, the decisivefactor is only that the relative location information is retained in thetransformation into the unity space. I.e. interrogation points which aredisposed in the origin space PS outside a segment object defined by thecontours C1, C2, are also disposed after transformation in the unityspace US with the aid of the transformation function TPS1 or TPS2outside the unity space segment object 20E. A corresponding pointcorrespondence is also provided for interrogation points on the surfaceor for interrogation points within the segment object defined by thecontours C1, C2.

A signed local distance function LF defined in the unity space US forthe surface of the unity space segment object 20E reproduces thislocation information for interrogation points in the unity space US.

For interrogation points of the origin space PS it is sufficient toobtain relative location information in relation to the segment object20 defined by the contours C1, C2, i.e. from the fact that theinterrogation point is also transformed with the aid of thetransformation function from the origin space PS into the unity space USand a distance with regard to the unity space segment object 20E isdetermined with the aid of the signed local distance function. Theleading sign of the local signed distance function in the unity space USreproduces this required relative location information.

This procedure thus makes it possible to assign relative locationinformation relating to a segment object 20 in the origin space PS to aninterrogation point in the origin space PS in a unique manner, withoutthe surface of the segment object 20 being described at all in theorigin space. An interpolation of segment objects 20 in the origin spacePS, i.e. for example in the global coordinate system, based on free-formcontours is thus not necessary for creating the relative locationinformation.

FIG. 14 shows a definition of a global indicator function forinterrogation points in the origin space PS, with the aid of which—asalready mentioned—various advantages can be obtained in the definitionof the boundary surface network. For example it can be defined whether afurther division of octree cells is sensible. In addition the globalindicator function can also be used for derivation of the boundarysurface network with the aid of the “marching cubes” method.

Each interrogation point which is disposed in the origin space PS withina bounding box 30 can be assigned a function value of the globalindicator function GIF. The bounding box encloses a number of contoursin the origin space PS, on the basis of which, in a number of unityspaces US, a unity space segment object 20E is assigned in each case. Inthis case each of the unity space segment objects 20E in the differentunity spaces US is assigned an individual transformation function TPS1,TPS2.

Distances from the surface of the unity space segment objects 20E in therespective unity space US are in this case likewise described by a localsigned distance function LF. In this case interrogation points which intheir turn lie in the unity space US within the volume of the unityspace segment object 20E, are assigned negative function values of thelocal signed distance function LF.

The global indicator function GIF for an interrogation point in thebounding box 30 is now determined by transformation of the interrogationpoint in each of the number of unity spaces US with the aid of theindividual transformation functions TPS1, TPS2 of the number of unityspace segment objects 20E. For the transformed interrogation point adistance value to the surface of the respective unity space segmentobject 20E can be calculated in each of the unity spaces US with the aidof the local signed distance function LF. The global indicator functionGIF is then assigned for the interrogation point of the minimal functionvalue of the local signed distance function LF related to thetransformed interrogation points. This includes the fact that only theleading sign of the minimal function value forms the global indicatorfunction GIF when the minimal function value is not zero. In a similarfashion the global indicator function GIF must also be formed on thebasis of the maximum of the local signed distance functions for thetransformed interrogation point, if the local signed distance functionLF assigns a positive distance value from the surface of the unity spacesegment object to interrogation points which lie within the volume ofthe unity space segment object 20E.

With the aid of the global indicator function GIF thus determined aboundary surface network can be quickly created, especially in themanner described in conjunction with FIG. 10. At the same time theglobal indicator function GIF represents a quick-to-calculate, unique,model-type description of the surface of complicated-shaped sections ofthe tubular object (namely simply through all points at which the globalindicator function GIF is zero), without complicated-shaped segmentobjects having to be interpolated for this purpose.

The fact that with this principle complicated sections, for examplebranches, of the tubular object are also taken into consideration, isillustrated particularly with the aid of FIGS. 15 to 17.

FIG. 15 again shows a section of an arterial vessel system in originspace PS as in FIG. 11. In this case in the center line presentation 10two contours C1, C2, especially directly following one another, aremarked in a branching area. A model-type description of this section ofthe arterial blood vessel system by segment objects 20 in the originspace PS would require the adaptation of a plurality of segment objects.The representation of this segment in the unity space US can on theother hand reduce the number of the segment objects needed and thus inits turn accelerate the definition of the boundary surface network.

As can especially be seen from the detailed segment depicted in FIG. 16(an enlargement of the dotted-line area from FIG. 15) of the arterialblood vessel system, the highlighted contours C1, C2 cross over eachother in the origin space PS. I.e. a very complicated segment objectwould have to be used here for local modeling in the origin space PSbetween the contours C1, C2.

FIG. 17 shows the transformation of the crossing contours C1, C2 fromthe origin space PS into the unity space US with the aid of anindividual transformation function TPS2. Here too the contours C1, C2are once more transformed to circular bounding edges K1, K2 in the unityspace. The bounding edges in this case again lie in the unity space USin a plane E1, E2 assigned to the respective bounding edge. These planesE1, E2 intersect (as in the origin space PS) in the unity space US at anangle, are thus disposed tilted in relation to one another, and thebounding edges K1, K2 have a number of common points (namely on theintersection line of the two planes E1, E2), as is also the case for theassociated contours C1, C2 in the origin space PS.

Furthermore bounding edges K1, K2 disposed tilted in relation to oneanother in the unity space US can only have one common point, i.e. ifthe bounding edges K1, K2 in the unity space US (and accordingly thecontours C1, C2 in the origin space PS) merely touch. In addition it isalso conceivable, for bounding edges disposed tilted in relation to oneanother, not to have any common point in the unity space, if for examplethe associated contours C1, C2 also do not intersect in the origin spacePS.

But in all these cases the surface of the unity space segment object 20Ethat is formed by tilted planes E1, E2 in the unity space can be formedand described in a simple manner. In this case unity space segmentobjects 20E always result, which in some sections at least, can bedescribed by surface sections of the outer surface of a truncated coneor of a cylinder. These outer surface sections define the shortestconnections between the different bounding edges K1, K2 in the unityspace US. This makes possible a simple description of the surface of theunity space segment object 20E, so that the described advantages of afast calculation of the signed local distance function LF can berealized therewith, which as described can be used for determining aboundary surface network of the signed distance function.

Finally FIG. 19 shows a rough schematic of a boundary surface networkdetermination system 300, with which, in the manner previouslydescribed, a determination of the boundary surface network can beundertaken. The boundary surface network determination system 300 ispreferably realized here on a computer system or a combination ofcomputer systems and comprises a division structure determination system380, which has an input interface 310 and a division structuredetermination unit 320 here.

With the aid of the input interface 310 a center line presentation 10determined on the basis of image data of the tubular object is recorded.This center line presentation 10 is available in the form of a datasetand is made available to the division structure determination system 300in digital form via the input interface 310. The center linepresentation 10 in this case, as described above, comprises contours ofthe tubular object lying in an origin space in an ordered series, towhich local dimension information 15 of the tubular object is linked.

Furthermore the input interface 310 can also be embodied to recordfurther settings of the delimitation network determination system 300 orof the division structure determination system 380, which a user canenter. For this purpose it can for example include a keyboard,touchscreen, mouse or similar or be linked to such a device. For examplethe “quality factor” mentioned can be provided to the system with theaid of the input interface 310, so that this value can be flexiblymodified by a user.

The center line presentation 10 recorded with the aid of the inputinterface 310 and also the local dimension information 15 is transferredto the division structure determination unit 320 which, based on thecenter line presentation 10 and the local dimension information 15, aspreviously described, determines and provides an octree 100 withdivision cells for the tubular object.

The boundary surface network determination system 300, also has asegment object determination unit 350, here as a part of the divisionstructure determination unit 320, which on the basis of consecutivecontours of the center line presentation 10 in each case, can determineone or more unity space segment objects 20E in a unity space. Thesegment object determination unit 350 is embodied, as explained above,to define for each of the unity space segment objects 20E a separatetransformation function TPS1, TPS2 from the origin space into the unityspace.

The unity space segment objects 20E as well is the definedtransformation functions TPS1, TPS2 are supplied to a distancedetermination unit 360 which calculates a local distance function in theunity space for each unity space segment object. The distancedetermination unit 360 further comprises a location determination unit365 which, as explained above, makes available a global indicatorfunction for interrogation points in the origin space on the basis ofthe local signed distance function.

All these components 350, 360, 365 of the division structuredetermination unit 320, even in the case of complicated free-formcontours as described above, still serve to obtain at least thenecessary relative location information for the different interrogationpoints very quickly, in order to be able to calculate the octree 100optimally. On the basis of the octree 100 a plurality of analyses canthen be undertaken and in particular a boundary surface network 1000 ofthe tubular object can be determined.

For this purpose the boundary surface determination system 300 comprisesa network determination unit 330. The octree 100 determined with the aidof the division structure determination system 300 is made available tothis network determination unit 330, which with the aid of the marchingcube algorithm on the basis of the octree 100, determines the desiredboundary surface network representation 1000 of the tubular object.

The boundary surface network 1000 thus determined is made available withthe aid of an output interface 340 to the user of the boundary surfacenetwork determination system 300. The output interface 340 can forexample involve a monitor or the like. Preferably however the boundarysurface network 1000 is supplied with the aid of the output interface340 to the memory, a network and/or a further processing device forfurther processing of the boundary surface network 1000.

The division structure determination system 380 and also the otherdescribed components of the boundary surface network determinationsystem 300 can be embodied individually or in combination, preferably assoftware components on a computer system.

It is clear from the previous description that, with the aid of theinvention, a boundary surface network with a tubular object can bedetermined with great speed and also with a (locally defined) highdegree of accurate detail. It is pointed out here that the features ofall example embodiments or developments disclosed in figures can be usedin any given combination. In conclusion it is likewise pointed out thatthe methods and systems described in detail above merely involve exampleembodiments, which can be modified by the person skilled in the art in avery wide variety of ways without departing from the field of theinvention. Furthermore the use of the indefinite article “a” or “an”does not preclude the features concerned also being present a number oftimes. Likewise the term “unit” does not preclude the componentsconcerned consisting of a number of interoperating subunits which ifnecessary can also be at different locations.

The example embodiment or each example embodiment should not beunderstood as a restriction of the invention. Rather, numerousvariations and modifications are possible in the context of the presentdisclosure, in particular those variants and combinations which can beinferred by the person skilled in the art with regard to achieving theobject for example by combination or modification of individual featuresor elements or method steps that are described in connection with thegeneral or specific part of the description and are contained in theclaims and/or the drawings, and, by way of combinable features, lead toa new subject matter or to new method steps or sequences of methodsteps, including insofar as they concern production, testing andoperating methods.

References back that are used in dependent claims indicate the furtherembodiment of the subject matter of the main claim by way of thefeatures of the respective dependent claim; they should not beunderstood as dispensing with obtaining independent protection of thesubject matter for the combinations of features in the referred-backdependent claims.

Furthermore, with regard to interpreting the claims, where a feature isconcretized in more specific detail in a subordinate claim, it should beassumed that such a restriction is not present in the respectivepreceding claims.

Since the subject matter of the dependent claims in relation to theprior art on the priority date may form separate and independentinventions, the applicant reserves the right to make them the subjectmatter of independent claims or divisional declarations. They mayfurthermore also contain independent inventions which have aconfiguration that is independent of the subject matters of thepreceding dependent claims.

Further, elements and/or features of different example embodiments maybe combined with each other and/or substituted for each other within thescope of this disclosure and appended claims.

Still further, any one of the above-described and other example featuresof the present invention may be embodied in the form of an apparatus,method, system, computer program, tangible computer readable medium andtangible computer program product. For example, of the aforementionedmethods may be embodied in the form of a system or device, including,but not limited to, any of the structure for performing the methodologyillustrated in the drawings.

Example embodiments being thus described, it will be obvious that thesame may be varied in many ways. Such variations are not to be regardedas a departure from the spirit and scope of the present invention, andall such modifications as would be obvious to one skilled in the art areintended to be included within the scope of the following claims.

What is claimed is:
 1. A method for determining a boundary surfacenetwork of a tubular object, comprising: providing a representation ofthe tubular object on the basis of image data; providing local dimensioninformation for points of the representation; creating a subdivideddivision structure presentation of the tubular object with divisioncells, based on the local dimension information including a differentspatial extent; and deriving the boundary surface network on the basisof the created division structure presentation.
 2. The method of claim1, wherein one or more local segment objects is adapted to therepresentation.
 3. The method of claim 2, wherein a topologicalstructure of the segment objects is selected from a group of primitives.4. The method of claim 1, wherein a spatial extent of a division cell isdefined at a location so that the division cell would be able to befitted completely into a local reference object, which is defined on thebasis of the local dimension so that it would be able to be fitted intothe tubular object or the local segment object at the location.
 5. Themethod of claim 1, wherein the representation comprises a center linepresentation of the tubular object including a number of center points,disposed at a distance from each other on a center line.
 6. The methodof claim 5, wherein local dimension information is given for centerpoints of the center line presentation.
 7. The method of claim 1,wherein the division structure comprises an octree and a division cellis formed by a cube-shaped spatial area.
 8. The method of claim 1,wherein, to create the division structure presentation, starting from astart division cell, a hierarchical subdivision of division sells isundertaken, wherein a division cell is not subdivided any further atleast one of if the division cell does not have any coverage with atleast one of a segment object and a bounding box which contains thesegment object, and if a local division threshold value is reached orundershot by the division cell.
 9. The method of claim 8, wherein thelocal division threshold value is based on the local dimensioninformation.
 10. The method of claim 9, wherein the local divisionthreshold value is defined from a number of division cells with the aidof a common scaling factor.
 11. The method of claim 8, wherein the localdivision threshold value is defined from a number of division cells withthe aid of a common scaling factor.
 12. The method of claim 8, wherein asigned distance function is determined for each segment object.
 13. Themethod of claim 12, wherein a global signed distance function isdetermined on the basis of a number of local signed distance functions.14. The method of claim 13, wherein the local division threshold valueis determined on the basis of at least one signed local distancefunction.
 15. The method of claim 14, wherein the local divisionthreshold value is determined on the basis of the global signed distancefunction.
 16. The method of claim 14, wherein the local divisionthreshold value is determined on the basis of the global signed distancefunction, and wherein, in a division cell for defining the localdivision threshold value, a value of at least one of the signed localdistance function and the global signed distance function is defined ina division cell center.
 17. The method of claim 12, wherein the localdivision threshold value is determined on the basis of at least onesigned local distance function.
 18. A non-transitory computer programproduct, loadable directly into one or more memories of a divisionstructure determination system, including program code sections forperforming the method of claim 1, when the program is executed in thedivision structure determination system.
 19. The method of claim 1,wherein a signed distance function is determined for each segmentobject.
 20. The method of claim 19, wherein a global signed distancefunction is determined on the basis of a number of local signed distancefunctions.
 21. The method of claim 20, wherein the local divisionthreshold value is determined on the basis of the global signed distancefunction.
 22. The method of claim 20, wherein the local divisionthreshold value is determined on the basis of the global signed distancefunction, and wherein, in a division cell for defining the localdivision threshold value, a value of at least one of the signed localdistance function and the global signed distance function is defined ina division cell center.
 23. A non-transitory computer readable mediumincluding program segments for, when executed on a division structuredetermination system, causing the division structure determinationsystem to implement the method of claim
 1. 24. A division structuredetermination system for determining a division structure presentationof a tubular object, the system comprising: an input interface,configured to provide a representation of the tubular object; an inputinterface, configured to provide local dimension information for pointsof the representation; and a processor and a memory, the memorycontaining computer readable code that, when executed by the processor,configures the processor as a division structure determination unit, thedivision structure determination unit configured to provide a subdivideddivision structure presentation of the tubular object with divisioncells which, based on the local dimension information, include adifferent spatial extent.
 25. A boundary surface network determinationsystem for determining a boundary surface network of a tubular object,comprising: the division structure determination system of claim 24; andan output interface configured to output a derived boundary surfacenetwork, wherein the processor is further configured as a networkdetermination unit, the network determination unit configured to derivethe boundary surface network on the basis of the division structurepresentation.